Theorem 2 (Redko et al. [1]}): Consider that a model is trained on the source domain, then for any \(d^{\prime }>d\)  and \(\zeta <\sqrt{2}\) , there exists a constant number \(N_0\)  depending on \(d^{\prime }\)  such that for any \(\xi >0\)  and \(\min (N,M)\ge \max (\xi ^{-(d^{\prime }+2),1})\)  with probability at least \(1-\xi \) , the following holds:
\(\begin{split}e_{\mathcal {T}}\le & e_{\mathcal {S}} +W(\hat{\mu }_{\mathcal {T}},\hat{\mu }_{\mathcal {S}})+e_{\mathcal {C}}(\mathbf {w}^*)+ \\& \sqrt{\big (2\log (\frac{1}{\xi })/\zeta \big )}\big (\sqrt{\frac{1}{N}}+\sqrt{\frac{1}{M}}\big ).\end{split}\) 
